Senior sources close to the consultant said Jeffries would present the shortlist to main board directors on Tuesday.
Jeffries has been acting chief executive since the departure of Robin Southwell last month after the group issued a profit warning and cut 400 jobs.
A source said: "The search for the new chief executive is well under way. Jeffries has a shortlist and that is due to go to the main board next week.
"Then it'll be taken from there and the best options explored."
Jeffries refused to comment because Atkins is due to present its results next month. He also refused to say how many were on the shortlist or whether they were from the industry. But he did concede soon after Southwell's resignation last month that the group needed a chief executive with an in-depth understanding of the industry and technical projects.
The search for the new chief executive is well under way
Atkins had been criticised by analysts and shareholders for appointing Southwell in April. Southwell had worked at weapons manufacturer BAE and had no experience of construction.
The sources also dismissed speculation that Atkins would be broken up and sold because of the group's debts and poor share price.
It had been suggested that management at its QS firm, Faithful & Gould, and property agency, Lambert Smith Hampton, were in talks with potential backers to prepare buy-out bids.
"Unless the management buy-out bids have the support of the board, they won't work," said the source. "The board has no intention of selling any part of the business so it doesn't matter how many meetings these people have with venture capitalists.
"All this talk in the press about sales and MBOs is very frustrating – and wrong. Atkins is pushing on."